Description of the class of strictly differentiable finite-state isometries of the ring $Z_2$

  • D. I. Morozov National University "Kyiv-Mohyla Academy"

Abstract

UDK 512+517.98

The condition of strict differentiability is a strengthening of the concept of differentiability, which is naturally applicable to the class of $p$-adic functions.
In this article, we study the strict differentiability of finite-state isometries of the ring $Z_2.$

 

References

L. Bartholdi, Z. Sunik, Some solvable automaton groups, Contemp. Math., 394, 11 – 29 (2006), https://doi.org/10.1090/conm/394/07431 DOI: https://doi.org/10.1090/conm/394/07431

R. I. Grigorchuk, V. V. Nekrashevich, V. I. Sushchanskii, Automata, dynamical systems and groups, Proc. Steklov Inst. Math., 231, 128 – 203 (2000).

N. Kobly`cz, $p$-Ady`chesky`e chy`sla,$ p$-ady`chesky`j analy`z y` dzeta-funkcy`y`, My`r, Moskva (1982).

D. I. Morozov, Izometriyi ta sty`skayuchi funkcziyi kil`cya $Z_2$, Visn. Zaporiz. nacz. un-tu, № 1, 90 – 97 (2014).

D. I. Morozov, Izometry`chnist` polinomiv nad kil`cem czily`x 2-ady`chny`x chy`sel, Nauk. zap. NaUKMA. Fiz.-mat. nauky`, 113, 13 – 15 (2011).

C. Weisman, On $p$-adic differentiability, J. Number Theory, 9, 79 – 86 (1977), https://doi.org/10.1016/0022-314X(77)90052-X DOI: https://doi.org/10.1016/0022-314X(77)90052-X

Published
16.09.2021
How to Cite
Morozov D. I. “Description of the Class of Strictly Differentiable Finite-State Isometries of the Ring $Z_2$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 9, Sept. 2021, pp. 1285 -88, doi:10.37863/umzh.v73i9.6106.
Section
Short communications